1. Field of the Invention
The present invention concerns a method to supplement MR data that were acquired with an accelerated acquisition method that undersamples k-space, as well as such a magnetic resonance system. Furthermore, the invention concerns an electronically readable data medium for implementing such a method.
2. Description of the Prior Art
Magnetic resonance tomography (MRT) is an imaging modality that enables the acquisition of two-dimensional or three-dimensional image data sets that can depict structures inside an examined person, in particular soft tissue as well, with high resolution. In MRT, protons in an examination subject are aligned in a basic magnetic field (B0) such that a macroscopic magnetization arises that is subsequently excited via the radiation of RF (radio-frequency) pulses. The decay of the excited magnetization is subsequently detected by one or more induction coils, wherein a spatial coding of the acquired MR signal can be achieved via the application of different magnetic field gradients (for slice selection, phase coding or frequency coding). The acquired MR signals initially exist in a positional (spatial) frequency space (also called k-space) and can be transformed into the image space by subsequent Fourier transformation. By the targeted switching (activation) of the magnetic field gradients, k-space can be scanned (i.e. data entered therein at respective data entry locations or points in k-space) with different trajectories, wherein a conventional scanning involves the successive acquisition of frequency-coded k-space lines (generally oriented along the X-axis of k-space) for different phase codings (that define the Y-axis of k-space).
In order to reduce the acquisition duration, for example given the acquisition of MR image data of a freely breathing examined person, various methods have been proposed that undersample k-space, meaning that they omit k-space lines or k-space points to be scanned, for example. Examples of such techniques are Generalized Auto-Calibrating Partially Parallel Acquisition (GRAPPA), Sensitivity Encoding (SENSE) and Simultaneous Acquisition of Spatial Harmonics (SMASH) imaging methods that are also generally designated as partially parallel acquisition (PPA) methods. For example, GRAPPA has the advantage that it is a self-calibrated method and only requires the inversion of a relatively small matrix to determine the parameters of the GRAPPA reconstruction kernel. However, the GRAPPA reconstruction kernel must be adapted to a defined scanning pattern (with which k-space is undersampled). Methods that apply arbitrary k-space trajectories to scan said k-space (and that by now are used in many imaging methods) can thus not be combined with the GRAPPA method without additional measures. Methods such as the monitoring of gradients or magnetic fields in order to determine actual k-space trajectories, k-space trajectories such as rosettes and spirals, and even random k-space trajectories increasingly arouse interest for use in imaging methods, but such acquisition methods cause irregular gaps or omissions in the acquired k-space data.
This can lead to the situation that multiple reconstruction seats must be provided in order to close a gap in k-space, but it is not always clear which reconstruction kernel should be selected to supplement the k-space data. The gaps or omissions in k-space can also be larger than the reconstruction kernels that are used, which can lead to the situation that such reconstruction kernel cannot completely close these gaps.
There are methods that, for example, have used a GRAPPA kernel to close gaps in k-space that are larger than the reconstruction kernel. A reconstruction kernel was thereby used that can extrapolate the k-space data in one direction, and this was repeatedly applied to the reconstructed data in order to close a larger k-space In this direction. A reconstruction kernel must in turn be selected that corresponds to the direction to be extrapolated, such that the k-space trajectories must be known. Furthermore, the reconstruction errors compound. Such a method also offers no solution for closing irregular gaps.
Furthermore, the MR data reconstructed with the reconstruction kernel can have relatively significant errors or noise. To reduce this, the data points of the reconstructed MR data for which MR data was actually measured are replaced with these measured data. However, such a procedure can lead to a degradation of the ultimately determined MR data, for example in cases in which the actual acquired MR data are severely plagued with noise.
Given an accelerated acquisition method, it is thus desirable to reconstruct supplemented MR data with optimally high precision, i.e. with optimally low noise. Furthermore, it is desirable to enable an optimally precise automatic reconstruction of MR data, even if the underlying produced MR data were acquired with an arbitrary k-space trajectory and/or if the reduced MR data have arbitrary—even larger or irregular—omissions or, respectively, gaps.